her:
I take it that the credit report you say seems OK is the credit report for the CRA that NatWest searched on? They are required to tell you if they searched a CRA and which one.
My advice is not to get hung up on the "credit score" number. It's not always relevent because your credit file does not include earnings data or non-credit outgoings, but given a good "score" the earnings and outgoings declared on your application are the main thing that the lender looks at. In other words the "affordability" is in the lenders eyes, not yours.
Credit is not guaranteed, sometimes they just don't want to. However the overdraft may not be doing you any favours. The bank can see whether or not you are paying it down and how fast. You don't say, but if you aren't I can see NatWest's point.
Later edit:
make sure that the £1000 you paid-off recently is on your credit report as it may take several weeks to show.